First slide

Fluid statics

Question

A sphere of solid material of relative density 9 has a concentric spherical cavity and Just sinks in water. If the radius of the sphere be R, then the radius of the cavity (r) will be related to R as

Easy

A

$r^{3} = \frac{8}{9} R^{3}$
B

$r^{3} = \frac{2}{3} R^{3}$
C

$r^{3} = \frac{\sqrt{8}}{3} R^{3}$
D

$r^{3} = \sqrt{(\frac{2}{3})} R^{3}$

Solution

Weight of the sphere = weight of water displaced
$(\frac{4}{3} {πR}^{3} - \frac{4}{3} {πr}^{3}) 9 \times g = \frac{4}{3} {πR}^{3} \times 1 \times g 9 R^{3} - R^{3} = 9 r^{3} or 9 r^{3} = 8 R^{3} ∴ r^{3} = (8 / 9) R^{3}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App